# A Macdonald refined topological vertex

## TL;DR

This paper introduces a Macdonald refined topological vertex by deforming the existing refined vertex with Macdonald parameters, unifying and extending previous topological vertex constructions with new deformation properties.

## Contribution

It defines a new Macdonald refined topological vertex that generalizes previous vertices and explores its limits and implications for 5D instanton partition functions.

## Key findings

- Recovers refined topological vertex as q -> t limit
- Obtains a qt-deformation of the topological vertex of Aganagic et al.
- Constructs qt-deformed 5D instanton partition functions with well-defined 4D limits

## Abstract

We consider the refined topological vertex of Iqbal et al, as a function of two parameters (x, y), and deform it by introducing Macdonald parameters (q, t), as in the work of Vuletic on plane partitions, to obtain 'a Macdonald refined topological vertex'. In the limit q -> t, we recover the refined topological vertex of Iqbal et al. In the limit x -> y, we obtain a qt-deformation of the topological vertex of Aganagic et al. Copies of the vertex can be glued to obtain qt-deformed 5D instanton partition functions that have well-defined 4D limits and, for generic values of (q, t), contain infinite-towers of poles for every pole in the limit q -> t.